The present invention relates to emission and reception of signals and to obtaining information regarding the signal path by obtaining information regarding the emitted and/or the received signals.
More particularly the present invention relates to a method for determining channel gain, wherein the received signal is transformed by means of a linear transform. The present invention further relates to a number of applications of the method, such as position determination of an emitter or of a reflective or refractive object, a pointing device for a computer, a door opening device, a remote control for e.g. an audio system, and reduction of xe2x80x9ccross talkxe2x80x9d in electrical components.
It is known to use wavelet transforms for transforming emitted and/or received signals. U.S. Pat. No. 5,384,725 (Coifman et al.) discloses a method and apparatus for encoding and decoding using wavelet-packets. This reference is concerned about the process of encoding/decoding a video or audio signal as such in order to compress/decompress the information contained in the signal. In particular this reference is concerned about finding the best basis for the wavelet transform to be used. The wavelet transform is used to transform an unknown signal.
Pointing devices for computers, such as the conventional xe2x80x9ccomputer mousexe2x80x9d or so-called xe2x80x9ctouch screensxe2x80x9d are known. However, the known devices require the hand of the user to be in a particular area in order to operate the device. This area is normally positioned in such a way that the user""s arm is put in a more or less awkward position, and the continuous use of such devices frequently results in overstrain of the muscles and/or other parts of the user. Furthermore, conventional pointing devices are normally confined to being moved in only two dimensions. Three dimensional movements of the pointer on the computer screen may be performed by means of such pointing devices. However, this is very difficult since it is not natural to perform three dimensional movements by moving a device in only two dimensions. So-called xe2x80x9ctouch screensxe2x80x9d require the user to actually touch the computer screen, thereby applying grease and/or other kinds of unwanted dirt to the screen.
It is desirable to be able to use a chosen linear transform to generate a particular signal, and to use the transform to obtain information relating to elements of the signal path. It is thus an object of the present invention to provide a method for obtaining such information when emitting and receiving signals. It is a further object of the present invention to provide an improved method of determining channel gain between one or more emitter(s) and one or more receiver(s), the method being fast as wells robust. It is an even further object of the invention to provide a method of determining channel gain between one or more emitter(s) and one or more receiver(s), wherein the battery power required is reduced as compared to known systems the received signal still being resolvable, even if it is very noisy. It is an even further object of the invention to provide a method for determining the position of an object placed in the signal path. It is an even further object of the present invention to provide a pointing device for a computer, the pointing device overcoming the above mentioned problems, in particular providing a more natural way of performing three dimensional movements on the computer screen. It is an even further object of the present invention to provide a method for eliminating or at least to a certain extend reducing the unintentional occurrence of a signal in one conductor of electronic equipment, the signal being intentionally present in another conductor of the equipment (so-called xe2x80x9ccross talkxe2x80x9d).
Thus, according to the present invention is provided a method for determining the channel gain(s) between one or more emitter(s) and one or more receiver(s), the method comprising the steps of
emitting a first output signal by means of a first emitter, the first output signal being deterministic and containing an interval of frequencies,
receiving a first input signal by means of a first receiver,
determining a transformed first input signal by transforming said first input signal by means of a predetermined linear transform,
determining a first channel gain by means of comparison of said transformed first input signal and a predetermined original first signal being equal to said first output signal being emitted and received noiselessly with a known channel gain and being transformed by means of said linear transform.
The first output signal is deterministic, i.e. it is not a completely random signal (such as xe2x80x9cwhite noisexe2x80x9d). It may, however, be a pseudo-random signal Preferably, the first output signal is a generated signal sequence which is generated before the emission step. The same sequence may be used every time the method is performed. The first output signal contains an interval of frequencies as opposed to a signal containing only a single frequency or a finite number of frequencies, such as a signal of the kind being emitted from conventional door openers, e.g. such as the ones known from super markets etc.
The linear transform is predetermined, i.e. it is chosen before the step of determining a transformed first input signal. The transform may be chosen initially, such as once and for all, so that the same transform is always used. Alternatively or additionally, a transform may be chosen each time the method is performed, i.e. the transform may be chosen dynamically based on the conditions of the current emission/reception of signals.
The comparison of the transformed first input signal and the original first signal may be a simple comparison of the signals, such as overlaying the signals and visually comparing them, or spectral subtraction of one signal from the other. It may alternatively or additionally be obtaining the inner product between the two signals.
The original first signal is equal to the first output signal being emitted and received noiselessly with a known channel gain and being transformed by means of the linear transform. The original first signal is thus preferably a synthetic signal which has been generated. This generated signal is then transformed by the inverse transform of the predetermined linear transform, emitted by the emitter (at this point it has xe2x80x9cbecomexe2x80x9d the first output signal), and received by the receiver (at this point it has xe2x80x9cbecomexe2x80x9d the first input signal). Thereby the comparison gives a measure of the noise which has been applied to the original signal from the emission (e.g. electrical noise in electrical components of the emitter), the transmission (e.g. reflection and/or refraction and/or absorption of at least part of the signal when travelling through a gas (e.g. atmospheric air or any other suitable gas) or when hitting one or more refractive and/or reflective and/or partially absorbing object(s)), and the reception (e.g. electrical noise in electrical components of the receiver). When in the present context the term xe2x80x9cnoise appliedxe2x80x9d is used, it should be understood as the intentional as well as the unintentional components being added to the signal during emitting/transmitting/receiving the signal. That is, it should be interpreted as comprising xe2x80x9cwantedxe2x80x9d information regarding the signal path, such as information originating from objects inserted in the signal path as well as xe2x80x9cunwantedxe2x80x9d regular noise, such as noise originating from external noise sources. The xe2x80x9cnoise appliedxe2x80x9d may even comprise the gain of the system, e.g. in form of a damping or an amplification.
Systematic errors (such as reflections from walls, or noise originating from external noise sources, such as remote controls, the sun, artificial light etc.) may be eliminated, or at least to a great extend reduced, by using the knowledge thus obtained, and information may be obtained regarding one or more object(s) which is/are inserted into the signal path. Most preferably, information relating to the reflective and/or refractive and/or absorbing characteristics of the object(s) is obtained.
The step of determining a transformed first input signal may further comprise the step of transforming said first input signal by means of at least a second predetermined linear transform.
In this case the first input signal is transformed using at least two different linear transforms. This may be an advantage if the first input signal comprises two or more components, e.g. originating from two or more different sources, such as two or more different emitters.
The step of determining a transformed first input signal may be performed by using a linear transform of full rank. Alternatively or additionally, it may be performed by using a convolution transform. In case the step of determining a transformed first input signal is performed by using a convolution transform, it may be performed by using a spectral transform or by using a spread spectrum transform. In case the step is performed by using a spectral transform, it may be performed by using a sine or cosine transform, such as a local sine or local cosine transform. Alternatively or additionally, the step may be performed by using a unitary transform, and/or a wavelet transform, and/or a Hadamard transform, and/or a Rudin-Shapiro transform, such as a symmetric Rudin-Shapiro transform.
In case a wavelet transform is used, and in case the basis chosen is linearly independent (or even orthogonal), it is very easy to determine at the receiver from which emitter (in case there is more than one) the received signal originates, even if the received signal is very noisy. Therefore, a minimum of battery power is needed at the emitter, since even a not very intensive signal will be resolvable at the receiver, since only very little actual information is needed at the receiver.
The method preferably, prior to emitting the first output signal, further comprises the step of transforming the predetermined original first signal by means of a linear transform being the inverse transform of the predetermined linear transform, thereby obtaining the first output signal as described above.
Preferably, the method further comprises the step of determining the original first signal from an obtained measure of noise applied to the first input signal. That is, an original first signal may be chosen according to the noise which is currently applied to emitted signals. The choice may e.g. be based on the characteristics of the noise, such as the frequency interval and/or the amplitude and/or the number of noise sources and/or other suitable characteristics of the noise. The first original signal may be specifically generated according to such characteristics each time the method is performed, or it may be chosen from a set of predetermined original first signals containing a finite number of different signals.
The xe2x80x9cnoisexe2x80x9d applied to the signal may also, apart from actual unwanted noise components of the signal, comprise information regarding one or more object(s), where it is desirable to obtain this information.
The measure of noise may be obtained from a comparison of a prior transformed first input signal and the respective prior original first signal. In this embodiment comparisons relating to prior emissions/receptions are stored, e.g. in a look-up table. In this manner information regarding systematic errors may be obtained, and such errors may thus be eliminated from the signal, as described above, so that only wanted xe2x80x9cnoisexe2x80x9d information remains.
Thus, the step of determining the original first signal may be performed repeatedly so as to obtain an adaptive determination of the channel gain.
The measure of noise may be obtained in a number of different ways. It may be done either before or after the transformation of the first input signal. The measure may be based upon e.g. the energy of the signal, the scattering of the signal, the entropy of the signal, the frequency content of the signal, the signal to noise ratio (SNR) of the signal, and/or any other suitable measure. These measures may be obtained from the full signal or from a part of the signal. Since the original first signal is known (only the intensity of this signal is unknown), it is further possible to, at least substantially, separate the received input signal into a component originating from the original signal and a noise component originating from different noise sources of the system. An appropriate guess of the intensity may be made thus giving a xe2x80x9csample-by-samplexe2x80x9d picture of the noise of the system, whereby the noise properties of the system may be determined.
Preferably the method further comprises the step of choosing a suitable transform for transforming the first input signal. This step is performed prior to the step of determining a transformed first input signal, and the choice is made based on a previously obtained measure of noise applied to the first input signal.
The previously obtained measure of noise applied to the first input signal may be obtained as described above. The transform may be chosen from a set of predetermined linear transforms containing a finite number of different linear transforms. The choice may be made in such a way that one type of linear transform is made when the environment is very noisy, and another transform is chosen when very little noise is present The choice is made in such a way that the comparison is as accurate as possible while at the same time ensuring that a not too large processing power will be required. Most preferably, a Rudin-Shapiro transform is chosen when the environment is very noisy, and a wavelet transform is chosen when very little noise is present.
The transform may be chosen before the first output signal is emitted or after the first input signal is received. In case the transform is chosen before the first output signal is emitted, the choice is most preferably made based upon measures of the noise of the system obtained by prior measurements as described above. In case the transform is chosen after the first input signal is received, the choice may alternatively or additionally be made based upon other appropriate factors, such as the noise currently being in the signal, the frequency content of the signal, and/or any other suitable measure as described above.
The step of emitting a first output signal may be performed by emitting an electromagnetic output signal or by emitting an-acoustic output signal. It may attentively or additionally be performed by emitting any other suitable output, such as a particle signal, e.g. electrons or xcex1-particles or any other suitable kind of particles, including photons, e.g. photons originating from radioactive decays or from fluorescence. Alternatively or additionally it may be performed by means of a water jet, the emitter in this case comprising a tap or the like for applying water to the emitter.
The step of receiving a first input signal may be performed by receiving an electromagnetic input signal or by receiving an acoustic input signal. It may alternatively or additionally be performed by receiving any other suitable output, such as a particle signal, e.g. electrons or xcex1-particles or any other suitable kind of particles, including photons, e.g. photons originating from radioactive decays or from fluorescence. Alternatively or additionally it may be performed by receiving a water jet.
Preferably, at least the transforming of the first input signal and the comparison of the transformed first input""signal and a predetermined original first signal is performed by means of digital processing means.
The digital processing means is preferably a computer device, such as a personal computer (PC), a DSP (dedicated hardware), or a terminal connected to a main frame system.
Preferably, the method further comprises the step of reflecting and/or transmitting the first output signal using an object, the step being performed prior to the step of receiving a first input signal.
Such an object could be any kind of suitable object, such as a solid object, e.g. the hand of a human being, a refractive object, such as a prism, a window, or an optic fibre, and/or a reflective object, such as a mirror or a wall, and/or it may be a suitable gas, where the gas maybe positioned in a gas cell or the like or it may even be atmospheric air. The object may be a xe2x80x9cblockerxe2x80x9d, i.e. an object which at least substantially prevents the output signal from reaching the receiver. In this case the receiver will normally receive a signal. As soon as it does no longer receive a signal, this indicates that an object is present in the signal path. This approach is advantageously employed when the purpose of detecting the presence of an object is to cause a door to be opened as will be further described below.
Most preferably, the method further comprises the step of obtaining information about the object. Such information may comprise information regarding the reflective and/or refractive and/or absorbing characteristics of the object. It may additionally or alternatively comprise information regarding the shape and/or colour and/or position and/or size and/or any other suitable information of the object, such as the mere presence of the object in a certain region.
In one embodiment of the present invention the step of obtaining information about the object comprises obtaining information regarding at least part of a human being.
Such information may relate to the position of the hand of a human being, in which case the information may be used as an input for a pointing device for a computer device or it may be used to indicate the presence: of the hand within a certain area, thus indicating, e.g., that a door should be opened in order to let the, person pass. This will be described in further detail below.
Alternatively or additionally, such information may relate to obtaining tomographic data of at least part of a human body. In this case the signals involved are preferably xcex3-rays and/or X-rays and/or ultra sound. The technique may further be used in scanning devices employing magnetic resonance (MR). In this embodiment a plurality of emitters and preferably a plurality of receivers will normally be employed, the emitters and receivers being substantially equally distributed around the region which is of interest. This will result in a scanning device giving a scanning result which comprises less noise than conventional scanners.
In a preferred embodiment the method further comprises, the steps of emitting a second output signal by means of a second emitter, the second signal being deterministic and containing an interval of frequencies,
receiving the first input signal by means of the first receiver,
determining the transformed first input signal by transforming said first input signal by means of a predetermined linear transform,
determining a second channel gain by means of comparison of said transformed first input signal and a predetermined original second signal being equal to said second output signal being emitted and received noiselessly and with a known channel gain,
wherein the predetermined original first signal and the predetermined original second signal are linearly independent.
In this embodiment two emitters and one receiver are employed.
In another preferred embodiment the method further comprises the steps of
receiving a second input signal by means of a second receiver,
determining a transformed second input signal by transforming said second input signal by means of a predetermined linear transform,
determining a second channel gain by means of comparison of said transformed second input signal and the predetermined original first signal being equal to said first output signal being emitted and received noiselessly and with a known channel gain.
In this embodiment two receivers and one emitter are employed.
In another preferred embodiment the method further comprises the steps of
emitting a second output signal by means of a second emitter, the second signal being deterministic and containing an interval of frequencies,
receiving a second input signal by means of a second receiver,
determining a transformed second input signal by transforming said second input signal by means of a predetermined linear transform,
determining a second channel gain by means of comparison of said transformed second input""signal and the predetermined original first signal,
determining a third channel gain by means of comparison of the transformed first input signal and a predetermined original second signal being equal to said second output signal being emitted and received noiselessly and with a known channel gain,
determining a fourth channel gain by means of comparison of the transformed second input signal and the predetermined original second signal,
wherein the predetermined original first signal and the predetermined original second signal are linearly independent.
In this embodiment two emitters and two receivers are employed.
In the three embodiments described immediately above it is possible to determine the position of an object being positioned in the signal paths.
In the embodiment where two emitters and two receivers are employed the step of emitting the first output signal and the step of emitting the second output signal may be performed by emitting signals being significant for each of the emitters.
It is thus possible to distinguish the signals so as to determine from which emitter they originated, thereby obtaining additional information regarding the signal paths. The significance may be obtained by making sure that the signals are orthogonal or at least linearly independent, and/or it may be obtained be letting the signals having different frequency intervals and/or different amplitudes and/or they may differ in any other suitable manner.
In a very preferred embodiment the method further comprises the steps of
emitting a plurality of output signals by means of a plurality of emitters, each of the plurality of signals being deterministic and containing an interval of frequencies,
receiving a plurality of input signals by means of a plurality of receivers,
determining a plurality of transformed input signals by transforming each of the input signals of said plurality of input signals by means of a predetermined linear transform,
determining a plurality of channel gains by means of comparison of said plurality of transformed input signals with each of a plurality of predetermined original signals each being equal to one of said plurality of output signals being emitted and received noiselessly and with a known channel gain,
wherein the predetermined original signals are linearly independent.
The predetermined original signals are preferably orthogonal.
Preferably, the step of emitting a plurality of output signals is performed by emitting signals being significant for each of the plurality of emitters as described above.
The method may further comprise the step of determining the position of an object based upon the determined channel gains. In this case the method may be used for providing an input to a pointing device for a computer device and/or it may be used for indicating the presence of a person, e.g. in front of a door, thereby causing the door to be opened in order to let the person pass.
The position of the object is preferably determined in three dimensions, but it may alternatively or additionally be positioned in two dimensions, in which case the movement of the object is normally confined to a certain plane. In this case the method may be used for providing an input to a pointing device for a computer device, the pointing device being similar to the known xe2x80x9ccomputer mousexe2x80x9d, but where the xe2x80x9cdevicexe2x80x9d which needs to be moved may be the hand or finger of the user, or it may be a xe2x80x9cpointing objectxe2x80x9d, such as a pen like object or a small sphere or any other suitable pointing object This gives a less awkward position of the hand of the user, thereby reducing the risk of the user getting strained muscles or the like. If the position of the object is determined in three dimensions this risk is even further reduced since the user may move his or her hand in a position which suits him or her, thereby making the movements even less awkward. Further, the pointer (i.e. the finger of the user or the suitable pointing object) is very easily moved in three dimensions, thereby providing a more natural way of operating a three dimensional pointer on the computer screen. This is very useful when graphical programmes, such as three dimensional computer games or architectural presentation programmes are used.
The method may further comprise the step of reflecting the emitted signing by the object, said step being performed after the step of emitting the signals, but before the step of receiving the signals.
The step of determining the position of an object may comprise the steps of
determining the channel gains,
determining relative distances of the object, said relative distances being based upon the determined channel gains,
converting the relative distances into a three dimensional position.
The relative distances are preferably the distances between each emitter and/or receiver and the object If the relative positions of the emitters/receivers are known, the position of the object is readily determined from these relative distances.
The step of converting the relative distances into a three dimensional position may be performed by means of a neural network and/or it may be performed by means of geometrical observations.
The method may even further comprise the step of determining the motion of the object and/or the spatial orientation of the object
The method may further comprise the steps of
detecting the presence of an object in the vicinity of at least one of the one or more emitter(s); and/or in the vicinity at least one of the one or more receiver(s) by means of comparing the determined channel gain with a predetermined threshold value,
performing a predetermined action in case the determined channel gain exceeds said predetermined threshold value.
The threshold value is very dependant on the situation, the characteristics of the object and on the kind of signal employed.
The predetermined action may be opening a door being in the vicinity of the object. In this case the xe2x80x9cobjectxe2x80x9d is preferably a person or a part of a person (such as the hand).
In an embodiment of the invention the step of emitting a first output signal is performed by using a movable emitter, and the step of receiving a first input signal is performed using at least two substantially stationary receivers, the method further comprising the steps of
determining the distance between the emitter and each of the receivers from the determined channel gains, and
determining the position of the emitter by combining the determined distances.
In another embodiment the step of emitting a first output signal is performed by using a movable emitter, and the step of receiving a first input signal is performed using at least three substantially stationary receivers, the method further comprising the steps of
determining the mutual ratios between the determined channel gains, and
determining the position of the emitter by combining the determined ratios.
The emitter may in the two above cases be a remote control for an audio and/or video system, or for any other suitable system. The method may in this case be employed for determining the position of the remote control, and, presuming that the person using the audio and/or video system is in the vicinity of the remote control, the position of this person. In the first mentioned embodiment the position is determined by a direct measurement of the distances between the emitter and each of the receivers. This requires a precise knowledge of the signal intensities. In the second mentioned embodiment only relative distances are measured, and this embodiment therefore does not require such precise knowledge.
As mentioned above, the emitter and the receivers are preferably comprised in an audio system, in which case the method further comprises the step of adjusting the loud speakers of the audio system according to the position of the first emitter, and thereby according to the position of the listener. This makes it possible to create an optimal sound environment around the listener, e.g. regarding the stereo effects and/or surround sound effects and/or the mutual volume of different components of the music (such as bass, treble, different instruments etc.).
In the following is given an example of the determining of the position of a movable emitter.
The following system determines the position of one emitter by means of several receivers. The emitter emits either a wavelet signal or a Rudin-Shapiro (RS) sequence. In both cases the various receivers receive the emitted signal at different times. If the receivers have synchronised sampling and the sampling rate is sufficiently high, the same signal will be present in all (or some) of the receivers, but delayed a number of samples depending on the distance between emitter and that particular receiver.
The wavelet transformed signal exhibits certain characteristics when delayed a number of samples, the characteristics depending on the delay. Thereby it is possible to determine the difference in time-of-flight (TOF) for the signal to each receiver, and it is a matter of geometrical or neural network means to determine the position of the emitter.
The auto correlation of the RS signal are small except for the zero shift, so by correlating the received RS signal with itself (or a xe2x80x9ccleanxe2x80x9d version of it) the zero shift correlation will be significantly larger than other shifts, thereby showing the delay of the received signal.
The two different principles apply primarily to acoustic signals, since the TOF is quite large (and therefore easier to determine by sampling) for sound compared to electromagnetic signals, which travel at the speed of light. Unfortunately, sound signals tend to be reflected well by the surroundings, and a number of echoes are expected to be received as well. However, no echo will be received by a receiver before the xe2x80x9cdirect pathxe2x80x9d signal has been received. Combined with the fact that the echoes are most unlikely to be as intensive as the xe2x80x9cdirect pathxe2x80x9d signal, it is possible to ignore/remove the echoes in the received signal.
By determining the position of more than one emitter, it is possible also to determine the orientation of an object, under the condition that the distances of the emitters are fixed with respect to each other. By determining position over time, it is possible to determine motion of an object.
The method may further comprise the steps of
inserting a time delay before the step of emitting the first output signal,
determining the contribution of the received input signal from other sources than the first output signal,
reducing said contribution of the received output signal.
In this case the step of determining the contribution of the received input signal from other sources than the first output signal is performed by correlation between the predetermined original first signal and the transformed first input signal.
The contribution from other sources than the first output signal may be originating from cross talk between electrical conductors on a printed circuit board, but it may attentively be originating from other sources, such as the reflection of the signal upon walls or other objects present in the room, and/or other non-relevant emitters, and/or radioactive sources, including the background radiation, and/or noise originating from emitters and/or receivers and/or any other suitable noise source.
The method may further comprise the step of obtaining information regarding the temperature of one or more parts of an object. The object may in this case be an object to be welded and the region being in the vicinity of the welding seam. This way it is possible to obtain information relating to the temperature of both sides of the welding seam, the arc and the melted material on the welded object. In this embodiment semiconductors are preferably employed, the semiconductors being sensible to electromagnetic radiation at wavelengths being characteristic for the current combination of material and temperature interval.
The energy, which heats the plasma and the air surrounding the arc as well as the material in the vicinity of the welding seam, originates from the applied current, which immediately heats the area in the vicinity of the arc, the heat being gradually transmitted to the melted material from there.
In order to separate the electromagnetic radiation originating from the two areas, the applied current is modulated by a suitable high frequent signal, which may preferably be generated using the wavelet transform. The part of the electromagnetic radiation received by the sensor which comprises a component of the emitted signal is presumed to originate from areas in the immediate vicinity of the arc, whereas the remaining part in particular will originate from the melted material If orthogonal signals are used mathematical characteristics of, e.g., the wavelet transform may be employed for removing noise and robustifying the separation of the two temperatures which it is desirable to determine.
The present invention further relates to a method for transmitting signals, the method comprising the steps of
selecting an output signal from a predetermined set of output signals,
emitting the selected output signal by means of the emitter,
receiving an input signal by means of a receiver,
determining a transformed input signal by transforming said input signal by means of a predetermined linear transform,
comparing the transformed input signal with a predetermined set of original signals, each of said original signals being equal to one of said output signals of the predetermined set of output signals being emitted and received noiselessly with a known channel gain and being transformed by means of said linear transform, and
identifying the selected first output signal from said comparison.
This embodiment of the present invention is particularly useful when the emitter is movable, e.g. a remote control for an audio and/or video system or for any other suitable kind of system. The predetermined set of output signals may in this case represent a number of different actions, such as xe2x80x9cplayxe2x80x9d, xe2x80x9cstopxe2x80x9d, xe2x80x9crepeatxe2x80x9d, xe2x80x9cvolume up/downxe2x80x9d etc., and emitting an output signal thus corresponds to sending a command to the audio/video system to perform the c6responding action. In a particular embodiment a receiver may additionally be comprised in the movable device, and an emitter may be positioned in the immediate vicinity of the receiver, so as to allow for two-way communication. In this case the system may return to the movable device a message regarding the reception of the command.
The present invention further relates to a pointing device for a computer comprising
emitter means for emitting one or more output signal(s), the signal(s) being deterministic and containing an interval of frequencies,
receiving means for receiving one or more input""signal(s),
first determining means for determining one or more transformed input signal(s), the first determining means comprising means for transforming said input signal(s) by means of a predetermined linear transform,
second determining means for determining one or more channel gain(s), the second determining means comprising means for comparison of said transformed input signal(s) and one or more predetermined original signal(s) each being equal to one of said output signal(s) being emitted and received noiselessly with a known channel gain and being transformed by means of said linear transform,
converting means for converting the determined channel gain(s) into a three dimensional position of an object, and for converting said three dimensional position into a position of the pointing device.
The object may be at least part of a human being, preferably the hand or the finger of the user of the pointing device as described above.
The pointing device may further comprise data communication means for communication between the pointing device and an external computer device. The data communication means may be wireless, or it may comprise one or more chords connecting the pointing device and the external computer device. The pointing device may alternatively constitute a part of the computer device.
The invention will now be further described by way of examples.